The Christoffel-Darboux Kernel & Applications


Newcastle University

Newcastle upon Tyne, UK

4-5 July 2022

The two-day event is aimed at promoting the Christoffel-Darboux kernel, a well known concept in approximation theory, as a versatile tool for applied areas of science, such as data analysis, dynamical systems or global optimization. The benefits of treating big data from the lens of the Christoffel-Darboux kernel are amply supported by recent advances in outlier detection, density estimation and manifold learning. Also, recent developments in non-convex, non-linear optimization single out the same kernel as an invaluable technical catalyst.


During the first day of the workshop four comprehensive lectures will introduce the non-expert participant to the theoretical and applied background of this promising, fast growing area of research.


The second day will be devoted to more specialized, seminar type discussions, including numerical experiments, explorations of real data and open questions.

Speakers

Jean-Bernard Lasserre LAAS-CNRS, University of Toulouse and ANITI Institute

Felix Kirschner Tilburg University

Etienne de Klerk Tilburg University

Monique Laurent CWI and Tilburg University

Edouard Pauwels University of Toulouse 3 Paul Sabatier and ANITI Institute

Mihai Putinar UC Santa Barbara and Newcastle University

Lucas Slot CWI

Venue

School of Mathematics, Statistics and Physics

Herschel Building

Lecture Theatre 2 (ground floor)
Newcastle University

With suggested accomodation at:

Motel One

Reference

The Christoffel-Darboux Kernel for Data Analysis

This volume offers foundational material for the topics covered by the workshop.

Schedule


Abstracts


Monday 4 July


09:30-10:30. Edouard Pauwels - Introduction to CD kernels and application in statistics

10:30-11:00. Coffee break

11:00-12:00. Jean-Bernard Lasserre - The CD-Kernel for retrieving the graph of a function and for interpolation

12:00-14:00. Lunch

14:00-15:00. Monique Laurent - Convergence analysis of sum-of-squares hierarchies in polynomial optimization

15:00-15:30. Coffee break

15:30-16:30. Etienne de Klerk - Construction of multivariate polynomial approximation kernels via semidefinite programming

19:00. Dinner at Marco Polo (please send a message to David Kimsey if you plan to attend)


Tuesday 5 July


09:30-10:30. Lucas Slot - Sum-of-squares hierarchies for polynomial optimization and the Christoffel-Darboux kernel

10:30-11:00. Coffee break

11:00-12:00. Mihai Putinar - The role of CD kernel in moment indeterminacy

12:00-14:00. Lunch

14:00-15:00. Edouard Pauwels - Emperical Christoffel Darboux Kernels and Applications

15:00-15:30. Coffee break

15:30-16:30. Felix Kirschner - Numerical aspects of constructive multivariate polynomial approximation kernels via semidefinite programming

Motel One - see the green pin

Herschel Building - see the red pin

Restaurants - see the purple pins:

Marco Polo (location for our Monday dinner)

Red Mezze

Tyneside Cinema

Early career researchers interested in participating with local financial support are kindly asked to send an e-mail to David Kimsey with a CV and a brief statement outlining the motivation for attending the meeting.


Registration: Registration is free, but if you intend to attend, please send an e-mail to David Kimsey.

If you are coming to the meeting and are interested in attending Monday night's dinner, please send a message to David Kimsey.

Funding for this meeting is gratefully acknowledged from the Heilbronn Institute for Mathematical Research, EPSRC and Newcastle University.

Organizers: David Kimsey, Mihai Putinar